Abstract
The paper presents an overview of theoretical aspects of ultrasound image
reconstruction techniques based on the circular Radon transform inversion.
Their potential application in ultrasonography in a similar way as it was
successfully done in the x-ray computer tomography is demonstrated. The
methods employing Radon transform were previously extensively explored in
the synthetic aperture radars, geophysics, and medical imaging using x-ray
computer tomography. In this paper the main attention is paid to the
ultrasound imaging employing monostatic transmit-receive configuration.
Specifically, a single transmit and receive omnidirectional source placed
at the same spatial location is used for generation of a wide-band
ultrasound pulse and detection of back-scattered waves. The paper presents
derivation of the closed-form solution of the CRT inversion algorithms by
two different approaches: the range-migration algorithm (RMA) and the
deconvolution algorithm (DA). Experimentally determined data of ultrasound
phantom obtained using a 32-element 5 MHz linear transducer array with
0.48 mm element pitch and 0.36 mm element width and 5 mm height, excited
by a 2 sine cycles burst pulse are used for comparison of images
reconstructed by the RMA, DA, and conventional synthetic aperture focusing
technique (SAFT). It is demonstrated that both the RMA and SAFT allow
better lateral resolution and visualization depth to be achieved as
compared to the DA approach. Comparison of the results obtained by the RMA
method and the SAFT indicates slight improvement of the lateral resolution
for the SAFT of approximately 1.5 and 1.6% at the depth of 12 and 32 mm,
respectively. Concurrently, however, the visualization depth increase for
the RMA is shown in comparison with the SAFT. Specifically, the scattered
echo amplitude increase by the factor of 1.36 and 1.12 at the depth of 22
and 32 mm is demonstrated. It is also shown that the RMA runs about 30%
faster than the SAFT and about 12% faster than the DA method
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